What is the difference between latent and embedding spaces?
Embedding vs Latent Space
Due to Machine Learning's recent and rapid renaissance, and the fact that it draws from many distinct areas of mathematics, statistics, and computer science, it often has a number of different terms for the same or similar concepts.
&quot;Latent space&quot; and &quot;embedding&quot; both refer to an (often lower-dimensional) representation of high-dimensional data:

Latent space refers specifically to the space from which the low-dimensional representation is drawn.
Embedding refers to the way the low-dimensional data is mapped to (&quot;embedded in&quot;) the original higher dimensional space.

For example, in this &quot;Swiss roll&quot; data, the 3d data on the left is sensibly modelled as a 2d manifold 'embedded' in 3d space. The function mapping the 'latent' 2d data to its 3d representation is the embedding, and the underlying 2d space itself is the latent space (or embedded space):

Synonyms
Depending on the specific impression you wish to give, &quot;embedding&quot; often goes by different terms:




Term
Context




dimensionality reduction
combating the &quot;curse of dimensionality&quot;


feature extraction feature projection feature embedding feature learning representation learning
extracting 'meaningful' features from raw data


embedding manifold learning latent feature representation
understanding the underlying topology of the data




However this is not a hard-and-fast rule, and they are often completely interchangeable.